Non-Stationary Markets

Forward-Oriented Causal Observables for Non-Stationary Financial Markets ArXiv ID: 2512.24621 “View on arXiv” Authors: Lucas A. Souza Abstract We study short-horizon forecasting in financial time series under strict causal constraints, treating the market as a non-stationary stochastic system in which any predictive observable must be computable online from information available up to the decision time. Rather than proposing a machine-learning predictor or a direct price-forecast model, we focus on \emph{“constructing”} an interpretable causal signal from heterogeneous micro-features that encode complementary aspects of the dynamics (momentum, volume pressure, trend acceleration, and volatility-normalized price location). The construction combines (i) causal centering, (ii) linear aggregation into a composite observable, (iii) causal stabilization via a one-dimensional Kalman filter, and (iv) an adaptive ``forward-like’’ operator that mixes the composite signal with a smoothed causal derivative term. The resulting observable is mapped into a transparent decision functional and evaluated through realized cumulative returns and turnover. An application to high-frequency EURUSDT (1-minute) illustrates that causally constructed observables can exhibit substantial economic relevance in specific regimes, while degrading under subsequent regime shifts, highlighting both the potential and the limitations of causal signal design in non-stationary markets. ...

Causal PDE-Control for Adaptive Portfolio Optimization under Partial Information ArXiv ID: 2509.09585 “View on arXiv” Authors: Alejandro Rodriguez Dominguez Abstract Classical portfolio models tend to degrade under structural breaks, whereas flexible machine-learning allocators often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that links structural causal drivers, nonlinear filtering, and forward-backward PDE control to produce robust, transparent allocation rules under partial information. The main contributions are: (i) construction of scenario-conditional risk-neutral measures on the observable filtration via filtering, with an associated martingale representation; (ii) a projection-divergence duality that quantifies stability costs when deviating from the causal driver span; (iii) a causal completeness condition showing when a finite driver span captures systematic premia; and (iv) conformal transport and smooth subspace evolution guaranteeing time-consistent projections on a moving driver manifold. Markowitz, CAPM/APT, and Black-Litterman arise as limit or constrained cases; reinforcement learning and deep hedging appear as unconstrained approximations once embedded in the same pricing-control geometry. On a U.S. equity panel with 300+ candidate drivers, CPCM solvers achieve higher performance, lower turnover, and more persistent premia than econometric and ML benchmarks, offering a rigorous and interpretable basis for dynamic asset allocation in nonstationary markets. ...